The centripetal force exerted on stunt motorcyclist Biker Bob while riding on the inner vertical surface of a circular track is?

Question

conceptional physics

Answer 1

That depends on where he is along the vertical track.  Suppose the cycle + rider mass is m and moving at speed v.  At the top of the vertical track, a downward normal force N and weight mg are pointing toward the center, and

 

F_c = mv²/r = N + mg

 

But at the bottom of the track, an upward normal force N' points toward the center while weight mg points away from the center.  If moving at speed v',

 

F_c' = mv'²/r = N' - mg

 

If he is in between the top and bottom, you have to account for the angle he sweeps when moving from the bottom to the top.  There just is no one single answer to this question.